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3cd1076 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 | #!/usr/bin/env python
# -*- coding: utf-8 -*-
import torch
import torch.nn as nn
import math
import os
import torch.distributed as dist
import torch.nn as nn
from torch import Tensor
def zeropower_via_newtonschulz5(G: Tensor, steps: int) -> Tensor:
"""
Newton-Schulz iteration to compute the zeroth power / orthogonalization of G. We opt to use a
quintic iteration whose coefficients are selected to maximize the slope at zero. For the purpose
of minimizing steps, it turns out to be empirically effective to keep increasing the slope at
zero even beyond the point where the iteration no longer converges all the way to one everywhere
on the interval. This iteration therefore does not produce UV^T but rather something like US'V^T
where S' is diagonal with S_{ii}' ~ Uniform(0.5, 1.5), which turns out not to hurt model
performance at all relative to UV^T, where USV^T = G is the SVD.
"""
assert G.ndim >= 2 # batched Muon implementation by @scottjmaddox, and put into practice in the record by @YouJiacheng
a, b, c = (3.4445, -4.7750, 2.0315)
X = G.bfloat16()
if G.size(-2) > G.size(-1):
X = X.mT
# Ensure spectral norm is at most 1
X = X / (X.norm(dim=(-2, -1), keepdim=True) + 1e-7)
# Perform the NS iterations
for _ in range(steps):
A = X @ X.mT
B = b * A + c * A @ A # quintic computation strategy adapted from suggestion by @jxbz, @leloykun, and @YouJiacheng
X = a * X + B @ X
if G.size(-2) > G.size(-1):
X = X.mT
return X
class Muon(torch.optim.Optimizer):
"""
Adam optimizer with orthogonalization step.
"""
def __init__(self, params, lr=0.001, betas=(0.9, 0.999), eps=1e-8, weight_decay=0, ns_steps=5):
defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, ns_steps=ns_steps)
super().__init__(params, defaults)
@torch.no_grad()
def step(self, closure=None):
"""
Performs a single optimization step.
Args:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss = None
if closure is not None:
loss = closure()
for group in self.param_groups:
for p in group['params']:
if p.grad is None:
continue
grad = p.grad
state = self.state[p]
# Initialize state
if len(state) == 0:
state['step'] = 0
state['exp_avg'] = torch.zeros_like(p)
state['exp_avg_sq'] = torch.zeros_like(p)
exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
beta1, beta2 = group['betas']
state['step'] += 1
bias_correction1 = 1 - beta1 ** state['step']
bias_correction2 = 1 - beta2 ** state['step']
# Update momentum and squared gradient
exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
# Compute the update
denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
step_size = group['lr'] / bias_correction1
# Orthogonalize the update
update = exp_avg / denom
if update.ndim >= 2:
update = zeropower_via_newtonschulz5(update, steps=group['ns_steps'])
# Apply the update
p.add_(update, alpha=-step_size)
# Apply weight decay
if group['weight_decay'] != 0:
p.add_(p, alpha=-group['lr'] * group['weight_decay'])
return loss |